1. **State the problem:** We have two parallel lines \(\ell\) and \(m\) cut by a transversal. The angles formed are \((2x + 20)^\circ\) on line \(\ell\) and \((6x + 24)^\circ\) on line \(m\). These angles are supplementary, meaning their sum is \(180^\circ\). We need to find \(x\) and verify the solution. 2. **Set up the equation:** Since the angles are supplementary, $$ (2x + 20) + (6x + 24) = 180 $$ 3. **Simplify the equation:** $$ 2x + 20 + 6x + 24 = 180 $$ $$ 8x + 44 = 180 $$ 4. **Solve for \(x\):** $$ 8x = 180 - 44 $$ $$ 8x = 136 $$ $$ x = \frac{136}{8} = 17 $$ 5. **Verify the solution:** Substitute \(x = 17\) back into the angles: $$ 2x + 20 = 2(17) + 20 = 34 + 20 = 54^\circ $$ $$ 6x + 24 = 6(17) + 24 = 102 + 24 = 126^\circ $$ Check if they are supplementary: $$ 54 + 126 = 180^\circ $$ This confirms the angles are supplementary and \(x = 17\) is correct.